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Q. No.Water of mass \(m\) gram is slowly heated to increase the temperature from \(T_1\) to \(T_2 .\) The change in entropy of the water, given specific heat of water is \(1~{Jkg}^{-1} {~K}^{-1},\) is
1. Zero
2. \(m \ln \left(\dfrac{T_1}{T_2}\right)~~\)
3. \({m}\left({~T}_2-{T}_1\right) \)
4. \(m \ln \left(\dfrac{T_2}{T_1}\right) \)
1. Zero
2. \(m \ln \left(\dfrac{T_1}{T_2}\right)~~\)
3. \({m}\left({~T}_2-{T}_1\right) \)
4. \(m \ln \left(\dfrac{T_2}{T_1}\right) \)
Subtopic: Second Law of Thermodynamics |
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Level 2: 60%+
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An ideal gas in a cylinder is separated by a piston in such a way that the entropy of one part is \({S_1}\) and that of the other part is \({S_2}.\) Given that \({S_1 > S_2.}\) If the piston is removed then the total entropy of the system will be:
1. \(S_1\text - S_2 \)
2. \(\frac{S_1}{S_2} \)
3. \(S_1 \times S_2 \)
4. \(S_1+S_2\)
1. \(S_1\text - S_2 \)
2. \(\frac{S_1}{S_2} \)
3. \(S_1 \times S_2 \)
4. \(S_1+S_2\)
Subtopic: Second Law of Thermodynamics |
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Level 1: 80%+
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A solid body has a constant heat capacity of \(1~\text{J K}^{-1}.\) It is heated from \(100~\text{K}\) to \(200~\text{K}\) in two different ways:
(i) By placing it successively in contact with \(2\) thermal reservoirs, each supplying the same amount of heat.
(ii) By placing it successively in contact with \(8\) thermal reservoirs, each supplying the same amount of heat.
The entropy changes of the body in cases (i) and (ii), respectively, are:
1. \(\ln2,~~4 \ln2 \)
2. \(\ln 2, ~~\ln 2 \)
3. \(\ln 2,~~2 \ln 2 \)
4. \(2 \ln 2,~~8 \ln 2\)
Subtopic: Second Law of Thermodynamics |
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